Is there a way to properly mirror an animation?
Add an Empty and place it in the same position where the origin point of your armature is. In Object Mode select your rig, then an Empty and press Ctrl+P.


Now select the Empty and scale it by -1 (S,X,-1).
Note that this may not be the proper way to do it. I think you should find the root bone (which controls all the other bones location) and rotate it by 180 degrees.